Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+2y &= 4 \\ 8x+2y &= 6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = -8x+6$ Divide both sides by $2$ to isolate $y$ $y = {-4x + 3}$ Substitute this expression for $y$ in the first equation. $-2x+2({-4x + 3}) = 4$ $-2x - 8x + 6 = 4$ Simplify by combining terms, then solve for $x$ $-10x + 6 = 4$ $-10x = -2$ $x = \dfrac{1}{5}$ Substitute $\dfrac{1}{5}$ for $x$ back into the top equation. $-2( \dfrac{1}{5})+2y = 4$ $-\dfrac{2}{5}+2y = 4$ $2y = \dfrac{22}{5}$ $y = \dfrac{11}{5}$ The solution is $\enspace x = \dfrac{1}{5}, \enspace y = \dfrac{11}{5}$.